#10 – The Banach–Tarski paradox
via www.garethmawer.com complain
Imagine that you are holding the ball. Now imagine that you started tear this ball into pieces, and they may be of any shape, which you like. After that you put the pieces together in a such way so you get two balls instead of one. What will be the size of the balls compared to original ball?
According to the theory of sets, the two balls will be the same size and shape as the original one. Furthermore, given that in this case balls have different volume, any of the balls can be converted in accordance with another. This leads to the conclusion that pea-sized ball can be divided into balls of the size of the Sun.
The trick of the paradox lies in the fact that you can break the balls into pieces of any shape. In practice it is impossible because the structure of the material, and ultimately the size of atoms place limitations.
#BanachTarski_paradox , #Petos_paradox , #Moravecs_paradox , #Benfords_Law , #C_paradox , #paradox , #Immortal_Ant , #Ecological_balance , #Tritone_paradox , #Mpemba_effect
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